The steady‐state temperature profiles in a magnetically confined cylindrical plasma obtained by balancing Ohmic power input and thermal diffusion are shown to exhibit a bifurcation as a function of the applied electric field. A linear stability analysis predicts that the upper (high temperature) branch is unstable and that the lower branch is stable. These results agree with those of a transport code that uses the steady‐state profiles as initial conditions. The transport calculation reveals that the upper solution decays to the lower solution with a growth rate that is in agreement with the linear stability computation.